Improved processes have been developed for atom (or group) transfer radical polymerization (ATRP). In one improvement, the ATRP process involves polymerizing in the presence of a (partially) free radical-deactivating amount of the corresponding reduced or oxidized transition metal compound. In a further improvement, the ATRP process involves polymerizing in a homogeneous system or in the presence of a solubilized initiating/catalytic system. The present invention also concerns end-functional, site-specific functional and telechelic homopolymers and copolymers; block, random, graft, alternating and tapered (or "gradient") copolymers which may have certain properties or a certain novel structure; star, comb and "hyperbranched" polymers and copolymers; multi-functional hyperbranched, end-functional polymers; cross-linked polymers and gels; water-soluble polymers and hydrogels (e.g., a copolymer prepared by radical copolymerization of a water-soluble monomer and a divinyl monomer); and an ATRP process using water as a medium.